Smooth Piecewise Polynomial Blending Operations for Implicit Shapes
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Date
2007
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Publisher
The Eurographics Association and Blackwell Publishing Ltd
Abstract
In this paper, we present a new set of blending operations for implicitly defined geometric shapes. The proposed shape operators are piecewise polynomial and blending range controllable, and can be constructed to any required degree of smoothness. The key idea behind these techniques is the introduction of the concept of the smooth absolute functions, which in turn lead to the definition of smooth maximum functions. These novel generalized absolute functions can be constructed recursively or through a recursively defined functions, and can thus be computed cheaply. In addition, the underlying mathematical descriptions of these shape operations are very simple and elegant.
Description
@article{10.1111:j.1467-8659.2007.01011.x,
journal = {Computer Graphics Forum},
title = {{Smooth Piecewise Polynomial Blending Operations for Implicit Shapes}},
author = {Li, Q.},
year = {2007},
publisher = {The Eurographics Association and Blackwell Publishing Ltd},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2007.01011.x}
}